So, we walked through this homework problem in class but I was not paying attention / sleeping and now I can't remember it. Bleh.

Let A ∈ GL[sub]n[/sub](R)

a) Prove that the characteristic polynomial of A has degree n

It's supposed to be done with induction and isn't terribly difficult ... I just made the mistake of sleeping or spacing out during nearly every single class for the past two months.

If someone could point me in the right direction without giving it away, I'd appreciate it.

Can you define stuff for us? It's been a while

GL[sub]n[/sub](R) ?

Also, is that a vector or a matrix? You're confusing with two different conventions (bold for vectors, cap letters for matricies).

GL[sub]n[/sub](R) = General Linear Group of matrices (basically just invertible n x n matrices). http://en.wikipedia.org/wiki/General_linear_group

And, it's a matrix. It shouldn't be bolded.

Here's stuff on characteristic polynomial

http://en.wikipedia.org/wiki/Characteristic_polynomial

There will always be a term in the determinant consisting of the product of all members on the main diagonal.

Also, the determinant can be performed as a recursive operation. Not sure how easy that is to generalize though.